Method for detecting at least one anomaly in an observed signal, corresponding computer program product and device

ABSTRACT

A method is provided for detecting the presence of an anomaly within an observed physical signal. The observed signal includes an addition of a physical disturbance signal and a reference signal. The anomaly is relative to a change in the behavior of the reference signal compared with a first tolerance value. Such a method includes: determining a time span having at least one moment of interest; detecting the presence of the anomaly within the observed physical signal during the time span by conducting a hypothesis test using the first tolerance value, a first rate of tolerated false alarms, and data obtained from processing the observed signal.

1. CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Section 371 National Stage Application ofInternational Application No. PCT/EP2013/056138, filed Mar. 22, 2013,the content of which is incorporated herein by reference in itsentirety, and published as WO 2013/139979 on Sep. 26, 2013, not inEnglish.

2. FIELD OF THE INVENTION

The field of the invention is that of the processing of a signalobserved via a measurement sensor.

More specifically, the invention relates to a technique for detecting atleast one anomaly present in the observed signal and related to theoccurrence of an unpredictable physical phenomenon.

The invention has many applications such as for example in the field ofmedicine and it can be implemented in devices for monitoring theprogress of a patient's physiological parameters.

More generally, it can be applied in all cases where the detection of ananomaly of a signal representing the progress of physical parameters isimportant for corrective operations to be performed subsequently.

3. TECHNOLOGICAL BACKGROUND

We shall strive more particularly here below in the document to describethe set of problems and issues that the inventors of the present patentapplication have confronted in the field of the monitoring of therespiratory flow of a patient on artificial respiration. It may berecalled that the respiratory flow corresponds to the volume of airflowing in the lungs per unit of time. The invention is naturally notlimited to this particular field of application but is of interest forany technique of monitoring that has to cope with similar or proximateproblems. Indeed, the present technique can be used to detect anomalies(also called irregularities or deviations) in relation to the “normal”(i.e. anomaly-free) behavior of any one of the following signals:

-   -   electrocardiogram (ECG) signals which are signals representing        the progress of the electrical potential that commands the        muscular activity of a patient's heart, as a function of time,        measured by electrodes placed on the surface of the patient's        skin;    -   electroencephalogram (EEG) signals which are signals        representing the progress of the electrical activity of the        brain, as a function of time, measured by electrodes placed on a        patient's scalp;    -   signals representing the progress of arterial pressure as a        function of time;    -   signals representing the progress of the oxygen concentration in        tissues as a function of time;    -   signals representing the progress of intracranial pressure.

This list is naturally not exhaustive and the present invention cannotbe limited only to these fields of application. Indeed, it can beapplied to any signal representing the progress of a patient'sphysiological parameters.

In the field of medical monitoring and artificial respiration, one vitalparameter for which special monitoring has to be performed is that ofmonitoring of curves of the flow and pressure in the air passages.Indeed, in the case of incomplete or limited expiration, especiallyamong patients with chronic obstructive pulmonary disease or withasthma, a phenomenon of air capture can arise causing thoracicdistension. Thus, the lung pressure (Auto-PEEP or intrinsic positive andexpiratory pressure) at the end of the expiration increases when such aphenomenon occurs. The presence of thoracic distension also results inthe respiratory flow not returning to zero before the next inspirationbegins.

This phenomenon of thoracic distension occurs in about 40% of patientsunder artificial respiration (or mechanical respiration) and it can havemany harmful, physical consequences. Depending of the level ofresistance and compliance of the patient's respiratory system, andtherefore his time constant, clinically significant thoracic distensioncan occur gradually within a period of a few minutes.

It may be recalled that the goal of artificial respiration (ormechanical respiration) is to assist or replace a patient's spontaneousrespiration if this respiration becomes inefficient or, in certaincases, totally absent. Artificial respiration is practiced mainly in thecase of critical care (emergency medicine, intensive or intermediatecare), but is also used in home care among patients having chronicrespiratory deficiency.

This means that the detection of thoracic distension (i.e. the detectionof Auto-PEEP) is important to enable the practitioner (or clinician) totake the action needed to reduce this phenomenon (for example bymodifying the ventilator settings and extending the expiratory time).

PEEPi can only be quantified at specific points in time through theperformance of an expiratory pause enabling measurement of theexpiratory equilibrium pressure.

The progress of intra-pulmonary pressure can however be deduced from ananalysis of the signal representing the progress of the air flow (inL/min) (i.e. the progress of the volume of the air inspired and expiredby the patient as a function of time, also called the respiratory flowcurve) of a patient measured through sensors positioned for example atthe ventilator. This means that a thoracic distension (i.e. anAuto-Peep) can be detected through the study of such a signal. FIGS.2(a) and 2(b) respectively present the characteristic phases (orsegments) of such a signal during a respiration cycle comprising aninspiration, a pause and an expiration and a signal representing theprogress of a patient's respiratory flow as a function of time, whichincludes a plurality of respiratory cycles.

There is a first technique known in the prior art, described in the USdocument US2010147305, called “System and Method for the AutomaticDetection of the Expiratory Flow Limitation”, which can be used, throughautomated processing, to detect a limitation of flow in the patient.

However, this technique has various drawbacks, especially that ofrequiring the integration of numerous sensors (entailing a large amountof dead space) as well as the use of regular variations of ventilatorparameters to enable this measurement. While this system can beenvisaged in spontaneous ventilation and during an exploration ofrespiratory function, its use in an artificial ventilation circuit seemsto be more complicated. Besides, this technique does not seem to becapable of enabling continuous and sequential analysis of the occurrenceof the phenomenon of distension and is not suited to the detection of athoracic distension related to a problem of interface between thepatient and the ventilator.

There is also another technique known in the prior art, applied to thedetection of anomalies in curves presenting the progress of the glucoselevel present in a patient's blood, described in the document by Y. Zhu,“Automatic Detection of Anomalies in Blood Glucose Using a MachineLearning Approach”, in IEEE International Conference on InformationReuse and Integration (IRI), 2010, which those skilled in the art couldapply to the present case.

In addition, there is another technique also known in the prior art,applied to the detection of anomalies in encephalograms described in thedocument by Wulsin et al., “Semi-Supervised Anomaly Detection for EEGWaveforms Using Deep Belief Nets”, Ninth International Conference onMachine Learning and Applications (ICMLA), 2010, which those skilled inthe art could apply to the present case.

Finally, there is also another technique known in the prior art appliedto the detection of anomalies described in the document by R. J. Riellaet al., “Method for automatic detection of wheezing in lung sounds”,Brazilian Journal of Medical and Biological Research (2009) 42: 674-684,which those skilled in the art could apply to the present case.

One major drawback of these techniques lies in the fact that theyrequire the implementation of a learning phase using a first data basefollowed by a validation phase using a second data base that isindependent of the first data base.

4. SUMMARY OF THE INVENTION

One particular embodiment of the invention proposes a method fordetecting the presence of an anomaly Δ(t) included in an observedphysical signal Y(t), said observed signal comprising an addition of aphysical disturbance signal X(t), and a reference signal ƒ(t), and saidanomaly being relative to a modification of the behavior of thereference signal ƒ(t) relative to a first tolerance value (τ,τ₀). Such amethod is characterized in that it comprises:

-   -   a step for determining a temporal set E comprising at least one        instant of interest (t_(k); {t₁, . . . , t_(K)});    -   a step for detecting the presence of said anomaly within said        observed physical signal in said temporal set E by carrying out        a hypothesis test using said first tolerance value (τ,τ₀), a        first rate of tolerated false alarms (γ₁), and data (p,Y)        obtained from a processing of the observed signal Y(t).

Thus, the general principle of the invention is that of carrying out ahypothesis test in order to detect such an anomaly.

Such a method makes it possible to achieve the above-mentioned goals.Thus, the use of such a method makes it possible to detect anomalies inreal time, and this is crucial in medical applications.

In addition, such an observed physical signal Y(t) represents theprogress of a patient's physiological parameters.

According to one particular aspect of the invention, such a method fordetecting is characterized in that the step for determining comprises:

-   -   a step for applying a wavelet transform to the observed signal        during a time of observation, said step for applying delivering        coefficients;    -   a step for comparing absolute values of said coefficients with a        first threshold where a function λ_(γ) ₂ (ρ) is the unique        solution in η of an equation 1−[Φ(η−ρ)−Φ(−η−ρ)]=γ₂, where a        function Φ(⋅) is the distribution function of a standard normal        random variable, γ₂ is a second rate of tolerated false alarms,        σ_(X) is the deviation of the noise X(t), L is a size of the        sample of said observed signal and a is a value close to        √{square root over (2 ln L)}, said step for comparing delivering        at least one instant of interest when the absolute value of one        of said coefficients is above said threshold λ_(SNT).

According to one particular aspect of the invention, such a method fordetecting is characterized in that the step for determining comprises afiltering step.

According to one particular aspect of the invention, such a method fordetecting is characterized in that it also comprises a step forsmoothing the observed signal.

According to one particular aspect of the invention, such a method fordetecting is characterized in that said step for detecting comprises:

-   -   a step for projecting the observed physical signal along a        vector of form p of the reference signal, said step for        projecting delivering a projected value u for said at least one        instant of interest (t_(k)); and    -   a step for comparing an absolute value of said projected value u        and a second threshold λ_(γ) ₁ *=Q_(|τ+w|)(1−γ₁) where γ₁ is        said rate of tolerated false alarms, τ is said first tolerance        value, Q is a quantile function of a random variable |τ+w| where        w is a projection of said physical disturbance signal, along        said vector of form p, said step for comparing corresponding to        said hypothesis test and enabling the detection of an anomaly        when the absolute value of said projected value u is above said        second threshold λ_(γ) ₁ *.

Thus, in this embodiment, such a hypothesis test uses only said firsttolerance value, said first rate of tolerated false alarms and said dataobtained from a processing of the observed signal. This hypothesis testtherefore does not necessitate the explicit knowledge of the model ofthe reference signal.

According to one particular aspect of the invention, such a method fordetecting is characterized in that when said set E comprises K instantsof interest (t₁, . . . t_(K)) and when the values of the source physicalsignal are correlated with these instants, said step for detectingcomprises:

-   -   a step for projecting the observed physical signal along a        vector of form p of the reference signal, said step for        projecting delivering a projected value u_(i) for each instant        of interest (t₁, . . . t_(K));    -   a first step for initializing a variable j at one;    -   a second step for initializing a variable u_(1:j) corresponding        to an average of j projected values;    -   a step for determining (705) the following elements: |u_(1:j)|,        λ_(1:j) ^((h)) and λ_(1:j) ^((l)) with λ_(1:j) ^((h))=Q_(|τ+w)        _(1:j) _(|)(1−γ₁), λ_(1:j) ^((l))=Q_(|τ+w) _(1:j) _(|)(γ₁) where        Q_(|τ+w) _(1:j) _(|)(⋅) is the quantile function of the random        variable |τ+w_(1:j)| where w_(1:j) corresponds to an average of        j projections of said physical disturbance signal along said        vector of form p;    -   a step for comparing (706) comprising comparisons between said        determined elements for an instant t_(j), and when        |u_(1:j)|>λ_(1:j) ^((h)) then an anomaly is detected, when        |u_(1:j)|≤λ_(1:j) ^((l)) then no deviation is detected and when        λ_(1:j) ^((l))<|u_(1:j)|≤λ_(1:j) ^((h)) the variable j is        incremented and the second step for initializing and the steps        for determining and comparing are reiterated.

Thus, in this embodiment, such a hypothesis test uses only said firsttolerance value, said first rate of tolerated false alarms and saidpieces of data obtained from a treatment of the observed signal. Thishypothesis test therefore does not necessitate the explicit knowledge ofthe model of the reference signal.

According to one particular aspect of the invention, such a method fordetecting is characterized in that the number of iterations of thesecond step for initializing and of the steps for determining andcomparing is limited by a given value M, smaller than K, and in that afinal test consisting in comparing |u_(1:M)| with only λ_(1:M) ^((h)) isdone, the test detecting an anomaly when |u_(1:M)|>λ_(1:M) ^((h)).

According to one particular aspect of the invention, such a method fordetecting is characterized in that said vector of form p of thereference signal is obtained by using a regression technique on thebasis of a model of the reference signal.

According to one particular aspect of the invention, such a method fordetecting is characterized in that said vector of form p of thereference signal is obtained by the use of a technique of estimationfrom the observed physical signal.

According to one particular aspect of the invention, such a method fordetecting is characterized in that, when said set E corresponds to atime span, said step for detecting comprises:

-   -   a step for obtaining a sample, sized L, of the observed signal;    -   a step for obtaining a sample, sized L, of the reference signal;    -   a step for determining a value corresponding to a norm of the        difference between the two samples obtained;    -   a step for comparing said value with a third threshold λ_(γ) ₁        *=λ_(γ) ₁ (τ) where the function λ_(γ) ₁ (ρ) corresponds to the        unique solution, in η, of the equation 1−R(ρ,η)=γ₁, where the        function R(ρ,⋅) corresponds to the distribution function of the        square root of any unspecified random variable according to a        non-centered χ² distribution law with L degrees of freedom and        defined by the parameter ρ², said step for comparing        corresponding to said hypothesis test and enabling the detection        of an anomaly when said value is greater than said third        threshold λ_(γ) ₁ *=λ_(γ) ₁ (τ).

According to one particular aspect of the invention, such a method fordetecting is characterized in that said observed signal corresponds to asignal belonging to the group comprising: a signal called anelectrocardiogram signal, a signal called a electroencephalogram signal,a signal representing a progress of arterial pressure, a signalrepresenting a progress of a concentration of oxygen in the tissues, asignal representing a progress of intra-cranial pressure, a signalrepresenting the progress of a respiratory flow.

According to one particular aspect of the invention, such a method fordetecting is characterized in that said physical disturbance signal X(t)is Gaussian.

Another embodiment of the invention proposes a computer program productcomprising program code instructions for the implementing of theabove-mentioned method (in any one of its different embodiments) whensaid program is executed by a computer.

Another embodiment of the invention proposes a computer-readable andnon-transient storage medium storing a computer program comprising a setof instructions executable by a computer to implement theabove-mentioned method (in any one of its different embodiments).

Another embodiment of the invention proposes a device for detecting thepresence of an anomaly Δ(t) included in an observed physical signalY(t), said observed signal comprising an addition of a physicaldisturbance signal X(t), and a reference signal ƒ(t), and said anomalybeing relative to a modification of the behavior of the reference signalƒ(t) relative to a first tolerance value (τ,τ₀). Such a device ischaracterized in that it comprises:

-   -   means for determining a temporal set E comprising at least one        instant of interest (t_(k); {t₁, . . . , t_(K)});    -   means for detecting the presence of said anomaly within said        observed physical signal, on said set by means of a performance        of a hypothesis test, using said first tolerance value (τ,τ₀), a        first rate of tolerated false alarms γ₁, and data (p,Y) obtained        from a treatment of the observed signal.

In another embodiment of the invention, such a detection device ischaracterized in that the detection means comprise:

-   -   means for projecting the observed physical signal along a vector        of form p of the reference signal, said means for projecting        delivering a projected value u for said at least one instant of        interest (t_(k)); and

means for comparing an absolute value of said projected value u and asecond threshold λ_(γ) ₁ *=Q_(|τ+w|)(1−γ₁) where γ₁ is said rate oftolerated false alarms, τ is said first value of tolerance, Q is aquantile function of a random variable |τ+w| where w is a projection ofsaid physical disturbance signal, along said vector of form p, saidmeans for comparing performing said hypothesis test and enabling thedetection of an anomaly when the absolute value of said projected valueu is above said second threshold λ_(γ) ₁ *

5. LIST OF FIGURES

Other features and advantages of the invention shall appear from thereading of the following description, given by way of an indicative andnon-exhaustive example and from the appended drawings, of which:

FIG. 1 presents a simplified architecture of a device for detectingAuto-Peep according to one particular embodiment of the invention;

FIG. 2(a) presents the characteristic phases of a signal during arespiration comprising an inspiration and an expiration;

FIG. 2(b) presents a signal representing the progress of the respiratoryflow of a patient as a function of time, said signal comprising aplurality of respiration cycles, as well as instants of interest for thedetection of Auto-Peep;

FIG. 3(a) presents the steps implemented by a module for detecting atleast one instant of interest t_(k) according to one particularembodiment of the invention;

FIG. 3(b) presents steps implemented by a module for detecting at leastone instant of interest t_(k) according to another particular embodimentof the invention;

FIGS. 4(a) and (b) present curves derived from the processing describedwith reference to FIG. 3(a);

FIGS. 5(a) and (b) present curves derived from the processing describedwith reference to FIG. 3(b);

FIG. 6 presents the steps implemented by a module for estimatingparameters according to one particular embodiment of the invention;

FIGS. 7(a), (b) and (c) present the organization, in the form offlowcharts, of the steps implemented by a module for detecting accordingto different embodiments of the invention.

6. DETAILED DESCRIPTION

In all the figures of the present invention, the identical elements andsteps are designated by a same numerical reference.

According to one embodiment, the invention is implemented by means ofsoftware and/or hardware components. From this perspective, the term“module” can correspond in this document equally well to a softwarecomponent, a hardware component or a set of hardware and softwarecomponents.

A software component corresponds to one or more computer programs or oneor more sub-programs of a program or more generally to any element of aprogram or of a piece of software capable of implementing a function ora set of functions according to what is described here below for theconcerned module. Such a software component is executed by a dataprocessor of a physical entity (terminal, server, gateway, etc) and iscapable of accessing the hardware resources of this physical entity(memories, recording media, communications buses, input/outputelectronic boards, user interfaces, etc).

In the same way, a hardware component corresponds to any element of ahardware unit capable of implementing a function or a set of functionsaccording what is described here below for the module concerned. It maybe a programmable hardware component or a component with integratedprocessor for executing software, for example, an integrated circuit, asmartcard, a memory card, an electronic board for executing firmware,etc.

FIG. 1 presents a simplified architecture of a device for detectingAuto-Peep according to one particular embodiment of the invention.

Such a device 100 for detecting Auto-Peep comprises:

-   -   a module 101 for acquiring data obtained by discretization, on        the basis of a sampling period T_(s), of an observed signal        Y(t)=θ(t)+X(t) where the signal X(t) is a noise coming from        errors caused by measurement apparatuses or external parasitic        events, and where the signal θ(t) is a signal of interest. More        specifically, it must be noted that the signal of interest        θ(t)=ƒ(t)+Δ(t) where ƒ(t) is a reference signal (i.e. the signal        without anomalies, as can be observed in a healthy patient) and        where Δ(t) corresponds to the signal representing anomalies        (i.e. Δ(t) can be interpreted as being a random process which        represents the manifestation of the anomalies that occur in a        patient). Such a module 101 thus enables the performance of the        formatting of the data thus acquired (and more specifically the        selection of a sub-part of the data received) as a function of a        temporal unit E (especially such a set can comprise one or more        precise instants of interest or such a set E can be a temporal        range of interest, i.e. a time span of interest) given to said        module 101 by a module 102 described here below;    -   a module 102 for determining a temporal set E. In this        embodiment, the module 102 determines at least one precise        instant of interest t_(k) on the basis of data obtained        previously, or same data acquired by the module 101 (thus, a set        is obtained corresponding either to E={t_(k)} or to E={t₁, . . .        , t_(K)} where t₁, t₂, . . . , t_(K) are particular instants        that are not necessarily consecutive). In one particular        embodiment, the module 102 gives a temporal range of interest        E=[t₀;t₀+T] to the module 101, where t₀ is an instant selected        by the module 102, and T is the temporal length of the temporal        range of interest (thus, such a temporal range corresponds to a        set of consecutive instants) in which at least one instant of        interest t_(k) is included. The module 102 carries out a        particular processing in order to detect at least one instant of        interest (i.e. one or more instants) as a function of        characteristics inherent to the signal of interest (for example        such a characteristic can be linked to the presence of a sudden        change such as sharp variation of the signal of interest when        this signal shows no anomalies (i.e. the reference signal)).        Thus, an instant of interest belonging to a set E={t_(k)} or        E={t₁, . . . , t_(K)} can be the instant starting from which        such a phenomenon of variation occurs. The temporal range of        interest E can correspond to the temporal range starting at the        instant from which such a phenomenon of variation occurs and        having a given length T (i.e. for example t₀=t_(k)). In one        particular embodiment of the invention, the reference signal        ƒ(t) presents patterns which are repeated in time (in this        embodiment, the module 102 does not need detailed knowledge of        the behavior of the reference signal ƒ(t) in detail (i.e. the        module 102 does not possess any module of the reference signal        ƒ(t)). In another embodiment, the module 102 possesses a model        of the reference signal ƒ(t);    -   a module 103 for estimating which, on the basis of the same        input data as the module 101 (namely the sampled signal as well        as the temporal set E coming from the module 102 for        determining), enables the estimation of different parameters        such as the form of the curve of the signal of interest on a        temporal range of interest (for example the form of the curve of        the signal of interest relative to the patterns that are        repeated as mentioned here above), a standard mean deviation or        the value at a precise instant of a temporal range;    -   a module 104 for detecting an anomaly in the signal of interest        θ(t) (for example an anomaly such as an Auto-Peep, i.e. when        Δ(t)>>0). In order to make such a detection of the formatted        data coming from the module 101, the module 104 requires the        estimations of different parameters coming from the module 103        as well as parameters of configuration (namely a rate of        tolerated false alarms γ₁ and a value of tolerance τ, the        utility of which will be described in detail further below in        the present application). Thus, the module 104 implements a        technique for detecting an anomaly within a signal of interest        θ(t) relative to a reference signal ƒ(t) in one or more precise        critical instants t_(k), or on a temporal range, this being done        on the basis of data coming from an observed signal Y(t).

It must be noted that, in one alternative embodiment, the functions ofthe modules referenced 101, 102, 103 and 104 can also be implemented inhardware form in a programmable component of an FPGA (Field ProgrammableGate Array) or ASIC (Application-Specific Integrated Circuit) type.

FIG. 2(a) presents the characteristic phases of a signal during arespiration comprising an inspiration and expiration.

Thus, during a respiration, the signal corresponding to the progress ofthe air flow inspired and expired by the patient can be segmented intothree distinct temporal ranges as a function of the behavior of such asignal. Such a segmentation corresponds to the three stages of arespiration, namely, an inspiration which is done during a firsttemporal range, then a pause during a second temporal range and anexpiration during a third temporal range. Thus, with reference to thedescription of the module 102, it must be noted that a temporal range ofinterest E=[t₀;t₀+T] can be one of these ranges.

FIG. 2(b) presents a signal representing the progress of the respiratoryflow of a patient as a function of time, said signal comprising aplurality of respiration cycles.

FIG. 3(a) presents steps implemented by a module for detecting at leastone instant of interest t_(k) according to one particular embodiment ofthe invention.

The module 102, in one embodiment, implements a step for decompositionof the observed signal received through the execution of a step 301 forapplying a wavelet transform to the observed signal (Y(t)) and then theexecution a step 302 for detecting a variation in the changing of thecoefficients obtained and of the corresponding instant or instants, indetecting especially the crossing of a threshold resulting from theimplementation of a hypothesis test. Thus, the module 102 can detect oneor more instants for which the behavior of the reference function or ofthe signal of interest has a particular characteristic (high variationetc) and therefore enables the definition of a temporal range ofinterest comprising for example this instant or these instants ofinterest.

More specifically, on a given time period, which is generally fairlylarge we have [T₁;T₂] where T₁ and T₂ represent times in which anobserved signal is discretized with a sampling period T_(s). Thus, inone embodiment, there is available a set of pointsy_(n)=Y(nT_(s))=θ(nT_(s))+X(nT_(s))=δ_(n)+x_(n) with n as an integer.For example, it is possible to obtain a sample of points of apredetermined size L. It must be noted that the discrete wavelettransform applied during the step 301 enables the transformation of Lgiven elements defined in time into L coefficients.

Thus, by choosing an orthonormal wavelet base g_(i), and because thedecomposition into wavelets is additive, the discrete wavelet transform(implemented by the module 102) on the sample sized L of the signalY=[y₁, . . . , y_(L)] makes it possible to obtain L coefficients (andmakes it possible to define a vector d=[d₁, . . . , d_(L)]) each ofwhich verify the following equation: d_(i)=α_(i)+β_(i), for i∈[[1;L]]where α_(i) corresponds to a wavelet coefficient of interest and β_(i)corresponds to a Gaussian noise.

Thus, the orthogonal matrix W associated with the discrete wavelettransform enables the following equalities to be verified: d=WY, α=Wδand β=WX where α=[α₁, . . . , α_(L)], β=[β₁, . . . , β_(L)], X=[x₁, . .. , x_(L)], Y=[y₁, . . . , y_(L)], δ=[δ₁, . . . , δ_(L)] and the matrixW has the dimension L×L. Depending on the hypotheses on the processingof edge problems, such a matrix can be orthogonal or “almostorthogonal”. In considering that the noise X(t) for which a sampleX=[x₁, . . . , x_(L)] is possessed can be likened to a Gaussian noise(even through the noise X(t) does not exactly possess the sameproperties as a Gaussian noise) and since the base on which theprojection is made is orthonormal, the noise X and the noise β have thesame probabilistic properties. Indeed, since β=WX, β inherits theGaussian nature of X, and Cov(β,β)=Eβ^(T)β=EX^(T)W^(T)W X=cov(X,X)=σ_(X)²I where σ_(X) is the mean standard deviation of the noise X.

At the exit from the step 301, a vector d=[d₁, . . . , d_(L)] istherefore obtained comprising L coefficients.

It must be noted that, when the sample is great (i.e. L is great), theabsolute value of the noise, i.e. the absolute value of any unspecifiedone of the Gaussian noises β_(i) is bounded, with a high probability, bya threshold value: λ_(u)(L)=σ_(X)√{square root over (2 lnL)}=σ_(β)√{square root over (2 ln L)} (in one particular embodiment ofthe invention, it is possible to choose another a threshold value thatis as close for example as λ_(u)(L)=σ_(X)√{square root over ((2 lnL−ln(ln L)))} or λ_(u)(L)=4σ_(X) (for large samples (L=4000))). Thisthreshold can also be interpreted as being the minimum value (in termsof absolute value) of the signal of interest. Consequently, the problemof detecting peaks and therefore of detecting associated instants ofinterest amounts to performing the following hypothesis test: (H₀):|d_(i)|>|λ_(u)(L)| relative to the hypothesis (H₁):|d_(i)|≤|λ_(u)(L)|.

Thus, the step 302 for detecting instants of interest (and thereforepossibly a temporal range of interest) comprises the following steps:

-   -   determining a first threshold

$\lambda_{SNT} = {\sigma_{X}{\lambda_{\gamma_{2}}\left( \frac{\lambda_{u}(L)}{\sigma_{X}} \right)}}$where λ_(γ) ₂ (ρ) is the unique solution in η of the following equation:1−[Φ(η−ρ)−Φ(−η−ρ)]=γ₂, where the function Φ(⋅) is the function ofdistribution of a standard normal random variable and γ₂ is a rate oftolerated or accepted false alarms. This rate is generally chosen to bevery small (for example γ₂=10⁻⁴ or 10⁻⁵ or 10⁻⁷, . . . );

-   -   comparing the value of |d_(i)| with the value of the first        threshold λ_(SNT). When the following condition is verified:        |d_(i)|>λ_(SNT) at a given instant, then a significant deviation        is detected at this instant. On the contrary, when the following        condition is verified: |d_(i)|≤λ_(SNT) then no significant        deviation is present at this given instant.

Thus, depending on the configuration of the module 102 by its user, itis possible to determine only a few precise instants grouped together ina temporal set E. It is also possible to define a temporal range ofinterest E comprising such a detected instant. In the event of detectionof numerous successive peaks, only the first instant will be consideredand the others will not be integrated with the temporal set.

In another embodiment, the module 102 carries out a preliminarytreatment on the observed signal (Y(t)) in order to obtain a smoothedobserved signal Y(t). The steps 301 and 302 are applied to a smoothedobserved signal of this kind Y(t).

FIGS. 4(a) and (b) present curves derived from the treatment describedwith reference to FIG. 3(a).

FIG. 3(b) presents steps implemented by a module for detecting at leastone instant of interest t_(k) according to another particular embodimentof the invention.

The module 102, according to this embodiment implements a step offiltration applied to the received observed signal. Thus, a step of thiskind enables the detection of one or more instants for which thebehavior of the reference function or of the signal of interest has aparticular characteristic (high variation, etc). Thus, a temporal rangeof interest can be defined through the use of a filtering step of thiskind.

More specifically, and in relation with a processing of a signal aspresented in FIG. 2(b), the instants of interest corresponding to theinstants pertaining to an end of expiration are detected automaticallyby the device 100 via the module 102 implementing such a filtering step.

In one particular embodiment of the invention, such a filtering stepcomprises:

-   -   a step 303 for smoothing the obtained signal Y(t)=θ(t)+X(t).        Thus, a smoothed observed signal Y(t) is detected;    -   a step for determining the sign 304 (positive or negative) of        the smoothed observed signal Y(t) (should the signal correspond        to a flow or air stream, the term “positive” sign is used when        the air stream occurs in a first direction and the “negative”        sign is used when the air stream occurs in the direction        opposite to the first direction), depending on a value of        tolerance Δ enabling the correction of the value of the sign        obtained (i.e. if at a given instant t, the smoothed observed        signal can be considered at first view to be a “positive” sign,        but if the value of the smoothed observed signal at this instant        is below a tolerance value Δ, then the observed signal will be        considered to be “negative”). More specifically, a step of this        kind consists in determining the progress of the function        sign(Y(t)−Δ) where the function sign(⋅) is the function        determining a sign (positive or negative expressed respectively        by the values +1 or −1). It must be noted that the tolerance        value Δ can be defined preliminarily by a clinician or estimated        from the representation of the function of distribution of the        air stream signal;    -   a step 305 for determining instants of interest via the        application of a filter F′ to the function sign(Y(t)−Δ)        determined at the previous step. The filter F′ corresponds for        example to the filter defined by F′=[−1, . . . , −1, +1, . . . ,        +1] as shown in FIG. 5(a). Such a filter makes it possible to        highlight the correlation of a plurality of samples. Thus, FIG.        5(b) and more specifically the graph at the bottom of FIG. 5(b)        presents the result of the determining of F′*sign(Y(t)−Δ) where        the peaks obtained 501, 502, 503, 504, 505 and 506 correspond to        the instants to be considered.

In another embodiment, when the reference signal ƒ(t) is periodic, it ispossible to obtain a temporal range of interest by carrying out atemporal segmentation relative to the reference signal ƒ(t) by usingtechniques based on the Markov chains (for example the SSMM (SegmentalSemi Markov Model) technique or the use of hidden Markov chains (HMM orHidden Markov Model)) which are implemented in the module 102.

FIG. 6 presents steps implemented by a module for estimating parametersaccording to one particular embodiment of the invention.

The module 103, using data relative to the observed signal as well as atemporal set coming from the module 102, executes several steps forestimating parameters that must then be transmitted to the decisionmodule 104.

The module 103 makes it possible, in one particular embodiment of theinvention, to carry out:

-   -   an estimation 601 of a vector p representing the form of the        reference signal ƒ(t) on a given time span linked to the        temporal set E;    -   an estimation 602 of the standard deviation σ_(X) of the noise        X(t);    -   an estimation 603 of a reference α_(PEP) enabling the        definition, from a given tolerance value τ₀, of a corrected        tolerance value τ₀+Δ_(PEP).

In a first embodiment, the step 601 for estimating the vector prepresenting the form of the reference signal ƒ(t) on a given time spancomprises:

-   -   a step for obtaining the model of the reference signal ƒ(t) on a        given time span comprising unknown parameters (for example on        the time span corresponding to the end of the phase of        expiration of air by a patient, such a reference signal is        modeled by the function ƒ(x)=a−be^(−ct) where b>0 and c>0. The        unknown parameters are the parameters a, b and c);    -   a step for applying a (non-linear) regression technique to the        data observed on the time span considered. Thus, from a set of        observation points (t_(i), y_(i)), the value of the        indeterminate parameters is determined (in this case, with        respect to the function ƒ(x)=a−be^(−ct) the parameters (a,b,c)        are determined, these parameters being the solution to the        following optimization problem

$\underset{a,b,c}{argmin}{\sum\limits_{i = 1}^{L}{w_{i}\left( {{y_{i} - \left( {a - {b\; e^{- {ct}_{i}}}} \right)^{2}},} \right.}}$where the significant values w_(i) are chosen so that the influence ofcertain points is reduced).

-   -   a step for determining the vector p from the result of the        previous step.

In a second embodiment, when the reference signal ƒ(t) has repetitivepatterns in time, the step of estimation 601 of the vector prepresenting the form of the reference signal ƒ(t) on a given time spancomprises a step for determining an estimation of such a vector{circumflex over (p)} from a sample of the data on a time span on whichno anomaly is present. For example, from a sample of 2L+1 elements (fora single respiration cycle), we have the vector {circumflex over(p)}=u₁=[{circumflex over (p)}_(−L), . . . , {circumflex over (p)}₀, . .. , {circumflex over (p)}_(L)]^(T) which corresponds to

$\left\lbrack {\frac{\hat{\theta}\left( {t_{k} - {LT}_{s}} \right)}{\hat{\theta}\left( t_{k} \right)},\ldots\;,1,\ldots\;,\frac{\hat{\theta}\left( {t_{k} + {LT}_{s}} \right)}{\hat{\theta}\left( t_{k} \right)}} \right\rbrack^{T}$and {circumflex over (θ)}(t_(k)±kT_(s))={circumflex over(ƒ)}(t_(k)±kT)). To obtain a more precise estimation, this step fordetermining is performed for K respiration cycles (without anomalies)and the estimation {circumflex over (p)} corresponds to the average ofthe estimations obtained.

Thus, we have

$\hat{p} = {\frac{1}{K}{\sum\limits_{i = 1}^{K}u_{i}}}$

In a third embodiment, the estimation 601 of the vector p can be madedynamically.

More specifically, in one embodiment of the invention, the vector ismodified in taking account of a parameter μ∈[0;1] to limit theimportance of the “former” estimation. Thus, we obtain

$\hat{p} = {\frac{1 - \mu}{1 - \mu^{K}}{\sum\limits_{i = 1}^{K}{\mu^{K - i}{u_{i}.}}}}$

The estimation 602 of the standard deviation σ_(X) of the noise X(t) canbe obtained according to any one of the two steps described here below.

The first step consists in carrying out an estimation through theapplication of a regression technique in considering the residuesobtained to be noise.

More specifically, for a single respiration cycle, from a sample of 2L+1elements, the sample being centered, we obtain a value

${\hat{\sigma}}_{X} = {\sigma_{1} = {\frac{1}{2L}{\sqrt{\sum\limits_{i = 0}^{2L}\left( {{f\left( {t_{k} - {\left( {L - i} \right)T_{s}}} \right)} - {\hat{\theta}\left( {t_{k} - {\left( {L - i} \right)T_{s}}} \right)}} \right)^{2}}.}}}$

To obtain a more precise estimation in the same way as for theestimation of the vector of form, it is appropriate to take the averageof the values of the deviation obtained for K cycles of respiration(without anomalies). Thus,

${\hat{\sigma}}_{X} = {\frac{1}{K}{\sum\limits_{i = 1}^{K}\sigma_{i}}}$

In a third embodiment, the estimation 602 of the standard deviationσ_(X) of the noise X(t) can be done dynamically.

More specifically, in one embodiment of the invention, the vector ismodified in taking account of a parameter μ∈[0;1] making it possible tolimit the importance of the “older” estimation. Thus, we obtain

${\hat{\sigma}}_{X} = {\frac{1 - \mu}{1 - \mu^{K}}{\sum\limits_{i = 1}^{K}{\mu^{K - i}{\sigma_{i}.}}}}$

The second step is a step for carrying out an estimation from thewavelet coefficients in using either a MAD (Median Absolute Deviation)type estimator or a DATE (d-dimensional adaptive trimming estimator)type estimator, when the noise X(t) is a Gaussian white noise or can beconsidered as capable of being likened to a Gaussian white noise. Thesetwo estimators (MAD or DATE) which use wavelet coefficients do not makeit necessary to obtain the model of the function ƒ unlike in the case ofthe previous technique.

The step of estimation 603 of a reference Δ_(PEP) enables thedefinition, from a given value of tolerance τ₀, of a corrected tolerancevalue τ=τ₀+Δ_(PEP) which will be used by the module 104.

More specifically, the reference Δ_(PEP) can be obtained by observing,at a given point of interest t_(k), the values of the signal of intereston several respiration cycles without anomalies, and by choosing Δ_(PEP)as being the mean value of these elements. Furthermore, this correctedtolerance value also had to be validated by the clinician. It is thereflection of a certain degree of limitation of the flow following thesettings on the ventilator (setting of an positive expiratorypressure—extrinsic PEP).

FIGS. 7(a), 7(b) and 7(c) are flowcharts presenting the arrangement ofthe steps implemented by a detection module according to differentembodiments of the invention.

FIG. 7(a) gives a view, in the form of a flowchart, of the arrangementof the steps implemented by a detection module according to oneembodiment of the invention, to detect an anomaly in the signal ofinterest at a precise instant t_(k).

The problem relating to the detection of a deviation between the signalof interest θ(t) and the reference signal ƒ(t) at a chosen criticalinstant t_(k), said deviation being considered as such as a function ofa tolerance value τ, can be formulated as the resolution of a testenabling a choice to be made between two hypotheses, H₀ and H₁, of whichone and only one is true, in the light of the formatted observed signalY(t) obtained through the module 101. The tolerance value τ is thereforea value for which it is considered that a deviation is or is notachieved. Thus, it is considered that when the difference (or deviation)in terms of absolute value between the signal of interest θ(t) and thereference signal ƒ(t) at a chosen critical instant t_(k) is greater thanthe tolerance value τ then a deviation has occurred. On the contrary, itis considered that when the difference (or the divergence) in terms ofabsolute value between the signal of interest θ(t) and the referencesignal ƒ(t) at a chosen critical instant t_(k) is below or equal to thetolerance value τ, then the deviation (or anomaly) does not occur. Thus,the tolerance value τ makes it possible not to consider small, marginalvariations of no importance in the signal of interest θ(t) compared withthe reference signal ƒ(t) at a chosen critical instant t_(k). The choiceof the tolerance value depends both on the value of the prior data aswell as on the practitioner's knowledge (see description of the step603).

Thus, it is appropriate, during a performance of such a test, to choosebetween the following hypotheses in the light of the formatted observedsignal Y(t): the hypothesis H₀ is that we have |θ(t_(k))−ƒ(t_(k))|>τ andthe hypothesis H₁ is that we have |θ(t_(k))−ƒ(t_(k))|≤τ.

In one embodiment of the invention, the chosen critical instant t_(k)being known (for example through the use of the module 102), the module101 can set up a formatting of 2L+1 samples of the observed signal inthe neighborhood of the chosen critical instant t_(k) and give such adata sample to the module 104. In one embodiment, the samples are notdistributed uniformly around the chosen critical instant t_(k). In apreferred embodiment, it is chosen to center the 2L+1 samples on eitherside of the chosen critical instant t_(k). Thus, assuming that asampling period T_(s) is chosen, the module 104, in one preferredembodiment of the module 101, obtains the 2L+1 samples of the observedsignal Y(t), put in the shape of a column vector Y=[Y(t_(k)−LT_(k)), . .. , Y(t_(k)−T_(s)), Y(t_(k)), Y(t_(k)+T_(s)), . . . ,Y(t_(k)+LT_(s))]^(T). By the definition of the observed signal, itbecomes the following vector equation Y=Θ+Ω where Θ=[θ(t_(k)−LT_(s)), .. . , θ(t_(k)), . . . , θ(t_(k)+LT_(s))]^(T) and Ω=[X(t_(k)−LT_(s)), . .. , X(t_(k)), . . . , X(t_(k)+LT_(s))]^(T).

When it can be established that Θ=[θ(t_(k)−LT_(s)), . . . , θ(t_(k)), .. . , θ(t_(k)+LT_(s))]^(T)=p·θ(t_(k))

with

$p = {\left\lbrack {p_{- L},\ldots\;,p_{0},\ldots\;,p_{L}} \right\rbrack^{T} = \left\lbrack {\frac{\theta\left( {t_{k} - {LT}_{s}} \right)}{\theta\left( t_{k} \right)},\ldots\;,1,\ldots\;,\frac{\theta\left( {t_{k} + {LT}_{s}} \right)}{\theta\left( t_{k} \right)}} \right\rbrack^{T}}$and where the vector p is known (because it is obtained through theestimation made by the module 103) a step of projection is carried outso that we have:

$\frac{p^{T}Y}{{p}_{2}^{2}} = {\frac{p^{T}\left( {\Theta + X} \right)}{{p}_{2}^{2}} = {\frac{p^{T}\left( {{p\;{\theta\left( t_{k} \right)}} + X} \right)}{{p}_{2}^{2}} = {{\theta\left( t_{c} \right)} + \frac{p^{T}X}{{p}_{2}^{2}}}}}$where the function ∥⋅∥₂ is the standard Euclidian norm.

Taking

${u = {{\frac{p^{T}Y}{{p}_{2}^{2}}\mspace{14mu}{and}\mspace{14mu} w} = \frac{p^{T}X}{{p}_{2}^{2}}}},$the equation is simplified as follows: u=θ(t_(k))+w. The step 701consists in determining the value of u in using especially theestimation of the vector p given by the module 103.

Thus, through the use of the vector p (to make the projection) or moreprecisely its estimation, the initially multidimensional problem becomesa one-dimensional problem.

In observing that the problem of the hypothesis test remains the same asabove, namely testing the hypothesis H₀: |θ(t_(k))−ƒ(t_(k))|>τ againstthe hypothesis H₁: |θ(t_(k))−ƒ(t_(k))|≤τ, and using “projected” data(i.e. u) and in observing that the variance of the noise

$w = \frac{p^{T}X}{{p}_{2}^{2}}$is smaller than that of the noise in t_(k), the test consists then inmaking a comparison of the value of |u| with a discrimination thresholdλ_(γ) ₁ * (which is a function of the rate of false alarms γ₁ toleratedor accepted by the practitioner and a tolerance value τ) which isobtained in a step 702 described here below. Thus, when the followingcondition is verified: |u|>λ_(γ) ₁ * then a significant deviation isdetected at the instant t_(k) within the signal of interest in complyingwith the rate of false alarms. On the contrary, when the followingcondition is verified: |u|≤λ_(γ) ₁ * then no significant deviation ispresent at the instant t_(k) within the signal of interest in complyingwith the rate of false alarms. Such a comparison is obtained during thestep 703.

The step 702 for determining the discrimination threshold λ_(γ) ₁ *consists in evaluating the quantile function Q of the random variable|τ+w| in the value (1−γ₁). It may be recalled that the quantile functionQ of the random variable |τ+w| is defined as follows:Q_(|τ+w|)(u)=inf({x/F_(|τ+w|)(x)≤u} where the function F_(|τ+w|)corresponds to the distribution function of the random variable |τ+w|,i.e. the function F_(|τ+w|) is defined as follows:F_(|τ+w|)(x)=P(|τ+w|≤x).

This means that obtaining the discrimination signal is done via thefollowing computation: λ_(γ) ₁ *=Q_(|τ+w|)(1−γ₁).

In one embodiment, when w is a centered Gaussian noise, the threshold ofdiscrimination is determined as follows:

$\lambda_{\gamma_{1}}^{*} = {\sigma_{w}{\lambda_{\gamma_{1}}\left( \frac{\tau}{\sigma_{w}} \right)}}$where the function λ_(γ) ₁ (ρ) is defined as being the single solution ηto the following equation: 1−[Φ(η−ρ)−Φ(−η−ρ)]=γ₁, where the functionΦ(⋅) is a function of distribution of a standard normal random variable.

FIG. 7(b) presents the arrangement, in the form of a flowchart, of thesteps implemented by a detection module according to one embodiment ofthe invention to detect an anomaly in a plurality of precise instantst_(k).

When the module 104 wishes to detect the presence of an anomaly in aplurality of precise instants t_(k) with k∈[[1;K]] included in thetemporal set E, it is necessary to ascertain whether the anomaliesoccurring at these instants are correlated or not. When these instantsare not correlated, it is enough to iteratively apply the stepsdescribed in relation with FIG. 7(a).

By contrast, when they are correlated (i.e. when similar repetitivepatterns are present at these instants), this information can be used toimprove the method of detection in the sense that the probability ofdetection of false alarms is reduced and the probability of detection ofanomalies is increased.

In this embodiment, the reference values at each of the instants t_(k)are considered to be identical (namely ƒ=ƒ(t₁)=ƒ(t₂)= . . . =ƒ(t_(K)))(it is always possible to return to such an embodiment even when thevalues of the ƒ(t_(i)) are not identical. Indeed, it is enough to choosea value ƒ as being the average of the value ƒ(t_(i)) and consider thatƒ=ƒ(t₁)=ƒ(t₂)= . . . =ƒ(t_(K))). In using the same technique ofprojection as the one described with reference to FIG. 7(a), we obtainu_(k)=θ(t_(k))+w_(k) for k∈[[1; K]] . . . then in taking the average weobtain u_(1:K)=θ_(1:K)+w_(1:K) with

${u_{1:K} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}u_{k}}}},{\theta_{1:K} = {{\frac{1}{K}{\sum\limits_{k = 1}^{K}{{\theta\left( t_{k} \right)}\mspace{14mu}{and}\mspace{14mu} w_{1:K}}}} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}{w_{k}.}}}}}$

Assuming that the reference signal does not vary excessively at the Kinstants t_(k) with k∈[[1;K]], the detection of an anomaly can be seenas a hypothesis test between the two following hypotheses:(H ₀): |θ_(1:K)−ƒ|>τ(H ₁): |θ_(1:K)−ƒ|≤τ

Depending on a rate of false alarms γ tolerated or accepted by thepractitioner, the decision rule is defined as follows:

If |u_(1:K)|>λ_(1:K) ^((h)) then an anomaly is detected;

If |u_(1:K)≤λ_(1:K) ^((l)) then no deviation is detected;

If λ_(1:K) ^((l))<|u_(1:K)|≤λ_(1:K) ^((h)) then no decision can be takenin the matter. The taking of the decision is postponed to a followinginstant.

The upper threshold λ_(1:K) ^((h)) is derived from the condition1−F_(|τ+w) _(1:K) _(|)(λ_(1:K) ^((h)))=γ₁.

The lower threshold λ_(1:K) ^((l)) is derived from the condition1−F_(|τ+w) _(1:K) _(|)(λ_(1:K) ^((l)))=1−γ₁.

Where the function F_(|τ+w) _(1:K) _(|)(⋅) corresponds to the functionof distribution of the random variable ∥τ+w_(1:K)∥. Thus, the twothresholds are computed as follows:λ_(1:K) ^((h)) =Q _(|τ+w) _(1:K) _(|)(1−γ₁)λ_(1:K) ^((l)) =Q _(|τ+w) _(1:K) _(|)(γ₁)

where Q_(|τ+w) _(1:K) _(|)(⋅) is the corresponding quantile function.

When the variable w_(1:K) is centered and Gaussian, we obtain theexplicit formulae below:

$\lambda_{1:K}^{(h)} = {\sigma_{w_{1:K}}{\lambda_{\gamma_{1}}\left( \frac{\tau}{\sigma_{w_{1:K}}} \right)}}$$\lambda_{1:K}^{(l)} = {\sigma_{w_{1:K}}{\lambda_{1 - \gamma_{1}}\left( \frac{\tau}{\sigma_{w_{1:K}}} \right)}}$

where λ_(γ)(ρ) is the only solution in η of the equation:1−[Φ(η−ρ)−Φ(−η−ρ)]=γ₁

and λ_(1−γ) ₁ (ρ) is the only solution in η of the equation:1−[Φ(η−ρ)−Φ(−η−ρ)]=1−γ₁, and the function Φ(⋅) is the function ofdistribution of a standard normal random variable. The element σ_(w)_(1:K) is considered to be obtained via the estimation module 103.

Thus, the method of detection of an anomaly comprises:

a step 704 for determining initialization of variables: j:=1;

a step 705 for determining the following elements: |u_(1:j)|, λ_(1:j)^((h))et λ_(1:j) ^((l));

a comparison step 706 for carrying out the following operations at aninstant t_(j).

If |u_(1:j)|>λ_(1:j) ^((h)) then an anomaly is detected;

If |u_(1:j)|≤λ_(1:j) ^((l)) then no deviation is detected;

If λ_(1:j) ^((l))<|u_(1:j)|≤λ_(1:j) ^((h)) then no deviation can betaken in this case. The taking of a decision is postponed to the testmade at a following instant. Thus, in this case, the variable j isincremented (i.e. j:=j+1), and the steps 705 and 706 are reiterated upto the processing of |u_(1:K)| if none of the preceding comparisons hasresulted in the detection of an anomaly.

So that the execution of such a decision method is not excessivelylengthy, it is preferable to limit the number of iterations so that adecision is taken up to a number M, and ultimately to carry out a finaltest for comparing |u_(1:M)| with only λ_(1:M) ^((h)).

If |u_(1:M)|>λ_(1:M) ^((h)) then an anomaly is detected, if|u_(1:M)|≤λ_(1:M) ^((h)) then no anomaly is detected.

FIG. 7(c) presents the arrangement, in the form of a flowchart, of thesteps implemented by a detection module according to one embodiment ofthe invention to detect an anomaly on a time span or a temporal rangeE=[t₀;t₀+T].

In one embodiment, the decision module 104 is considered to obtain:

-   -   a sample of L data of the observed signal Y=[y₁, . . . , y_(L)],        coming from the module 101;    -   a sample of L data of the reference signal F=[ƒ₁, . . . , ƒ_(L)]        (where ƒ_(k)=ƒ(k·T_(s))), obtained either via the estimation        module 103 (if the reference signal is periodic) or, if there is        a modeling of the reference signal available, it is obtained by        the application of such a model. Thus, this embodiment requires        the use of a sample of the reference module unlike in the other        two embodiments.

The problem pertaining to the detection of a deviation between thesignal of interest θ(t) and the reference signal ƒ(t) on a given timespan E=[t₀;t₀+T] amounts to making the following hypothesis testconsisting in choosing between the following two hypotheses in the lightof the formatted observed signal Y(t): the hypothesis H₀ is that we have∥Y−F∥>τ and the hypothesis H₁ is that we have ∥Y−F∥≤τ.

A Mahalanobis norm is chosen defined for a vector v, with the dimensionL, as follows: ∥v∥=(v^(T)C⁻¹v)^(1/2) where C is the matrix of covarianceof the signal noise.

In one embodiment of the invention, this matrix is deemed to be known.

In another embodiment of the invention, it is considered that thismatrix is obtained via an estimation step in assuming that the noise ofthe signal is colored.

Depending on the rate of false alarms γ tolerated or accepted by thepractitioner, it is possible to detect an anomaly on the given time spanE=[t₀;t₀+T] by comparing, at a step 709, the value of ∥Y−F∥, obtainedduring a step 707 with a threshold λ_(y) ₁ * which is determined in astep 708 which is described here below. Thus, when ∥Y−F∥>λ_(γ) ₁ *, itmeans that an anomaly is present on a given time span E=[t₀;t₀+T]. And,on the contrary, when ∥Y−F∥≤λ_(γ) ₁ *, it means that no anomaly ispresent on the given time span E=[t₀;t₀+T].

The threshold λ_(γ) ₁ * determined during the step 708 is derived fromthe following condition: 1−F_(∥Δ+X∥)(λ_(γ)*)≤γ₁ for any value of Δverifying ∥Δ∥≤τ, where the function F_(|Δ+X∥) corresponds to thefunction of distribution of the random variable ∥Δ+X∥.

Thus, the step 708 for determining the threshold λ_(γ) ₁ * comprises astep for determining the unique element η of the equation 1−R(ρ,η)=γ₁,corresponding to λ_(γ) ₁ (ρ), then a step for determining λ_(γ) ₁*=λ_(γ) ₁ (τ) and where the function R(ρ,⋅) corresponds to thedistribution function of the square root of any unspecified randomvariable according to a law of non-centered χ² distribution with Ldegrees of freedom and defined by the parameters ρ².

At least one embodiment of the present disclosure provides a techniquefor detecting anomalies in a signal (respiratory flow curve, etc) thatis precise.

At least one embodiment of the present disclosure provides a techniqueof this kind that can be easily configured by a user.

At least one embodiment of the present disclosure provides a techniqueof this kind that works in real time.

At least one embodiment of the present disclosure provides a techniqueof this kind that costs little to implement.

At least one embodiment of the present disclosure provides a techniqueof this kind that does not require the implementing of automaticlearning techniques.

At least one embodiment of the present disclosure provides a techniqueof this kind that does not require the use of data bases.

At least one embodiment of the present disclosure provides a techniqueof this kind that can be implemented without the use of intrusivemethods.

At least one embodiment of the present disclosure provides a techniqueof this kind that does not require the use of the dispatch of anothersignal, such a technique being possibly qualified as a passivetechnique.

At least one embodiment of the present disclosure provides a techniqueof this kind that is simple to implement.

At least one embodiment of the present disclosure provides a techniqueof this kind that does not require the use of a plurality of sensors.

At least one embodiment of the present disclosure provides a techniqueof this kind that can be applied to numerous types of signals.

Although the present disclosure has been described with reference to oneor more examples, workers skilled in the art will recognize that changesmay be made in form and detail without departing from the scope of thedisclosure and/or the appended claims.

The invention claimed is:
 1. A method for detecting an anomaly inrespiratory flow of a patient on artificial respiration comprising:receiving an observed physical signal by a detecting device of arespiratory flow of a patient on artificial respiration, the observedsignal including respiration stages of the respiratory flow including aninspiration during a first temporal range, which is followed by a pauseduring second temporal range, which is followed by an expiration duringa third temporal range; and detecting, by the detecting device, presenceof an anomaly Δ(t) included in the observed physical signal Y(t), whichrepresents progress of a patient's physiological parameters, saidobserved physical signal comprising an addition of a physicaldisturbance signal X(t), and a reference signal ƒ(t), and said anomalybeing related to a modification of the reference signal ƒ(t) relative toa first predetermined tolerance value (τ,τ₀), wherein detectingcomprises the following acts performed by a data processor of thedetecting device: determining a temporal set E comprising at least oneinstant of interest (t_(k); {t₁, . . . , t_(K)}), wherein the temporalset E corresponds to one of the first, second or third temporal ranges;and detecting the presence of said anomaly within said observed physicalsignal in said temporal set E by carrying out a hypothesis test usingsaid first predetermined tolerance value (τ,τ₀), a first rate oftolerated false alarms (γ₁), and data (p,Y) obtained from a processingof the observed signal Y(t).
 2. The method according to claim 1, whereindetermining further comprises: obtaining coefficients by applying awavelet transform to the observed signal during a time of observation;obtaining said at least one instant of interest when the absolute valueof one of said coefficients is above a first threshold λ_(SNT) bycomparing the absolute values of said coefficients with the firstthreshold where: λ_(SNT)=σ_(X)λ_(γ) ₂ (ρ) and where$\rho = {\left( \frac{\lambda_{u}(L)}{\sigma_{X}} \right)\mspace{14mu}{and}\mspace{14mu}{\lambda_{\gamma_{2}}(\rho)}}$and λ_(γ) ₂ (ρ) is the unique solution in η of the following equation:1−[Φ(η−ρ)−Φ(−η−Σ)]=γ₂, where the function Φ(⋅) is the function ofdistribution of a standard normal random variable, γ₂ is a second rateof tolerated false alarms, σ_(X) is the deviation of the noise X(t), Lis a size of the sample of said observed signal and a is approximately√{square root over (2 ln L)}.
 3. The method according to claim 2,wherein detecting further comprises: obtaining a projected value u forsaid at least one instant of interest (t_(k)) by projecting the observedphysical signal along a vector of form p of the reference signal; anddetecting said anomaly when an absolute value of said projected value uis above a second threshold λ_(γ) ₁ *=Q_(|τ+w|)(1−γ₁) where γ₁ is saidrate of tolerated false alarms, τ is said first tolerance value, Q is aquantile function of a variable |τ+w| where w is a projection of saidphysical disturbance signal, along said vector of form p.
 4. The methodaccording to claim 3, wherein said vector of form p of the referencesignal is obtained by using a regression technique on the basis of amodel of the reference signal.
 5. The method according to claim 3,wherein said vector of form p of the reference signal is obtained byusing a technique of estimation from the observed physical signal. 6.The method according to claim 1 wherein determining further comprises afiltering step.
 7. The method according to claim 1, wherein the methodfurther comprises smoothing the observed signal.
 8. The method accordingto claim 1, wherein, when said set E comprises K instants of interest(t₁, . . . t_(K)) and when the values of the observed physical signalare correlated with these instants, said detecting further comprises:obtaining a projected value u₁ for each instant of interest (t₁, . . .t_(K)) by projecting the observed physical signal along a vector of formp of the reference signal; initializing a variable j at one;initializing a variable u_(1:j) corresponding to an average of jprojected values; determining the following elements: |u_(1:j)|, λ_(1:j)^((h)) and λ_(1:j) ^((l)) with λ_(1:j) ^((h))=Q_(|τ+w) _(1:j)_(|)(1−γ₁), λ_(1:j) ^((l))=Q_(|τ+w) _(1:j) _(|)(γ₁) where Q_(|τ+w)_(1:j) _(|)(⋅) is the quantile function of the variable |τ+w_(1:j)|where w_(1:j) corresponds to an average of j projections of saidphysical disturbance signal along said vector of form p; comparing saiddetermined elements for an instant t_(j), and when |u_(1:j)|>λ_(1:j)^((h)) then the anomaly is detected, when |u_(1:j)|≤λ_(1:j) ^((l)) thenno deviation is detected and when λ_(1:j) ^((l))<|u_(1:j)|≤λ_(1:j)^((h)) then the variable j is incremented and the acts of initializing,determining and comparing are reiterated.
 9. The method according toclaim 8, wherein the number of iterations of the initializing thevariables j and u_(1:j), determining and comparing is limited by a givenvalue M, smaller than K, and wherein a final test comprising comparing|u_(1:M)| with only λ_(1:M) ^((h)) is done, the test detecting theanomaly when |u_(1:M)|>λ_(1:M) ^((h)).
 10. The method according to claim1, wherein when said set E corresponds to a time span (E=[t₀;t₀+T])where T represents the temporal length of said time span, said detectingcomprises: obtaining a sample, sized L, of the observed signal (Y=[y₁, .. . , y_(L)]); obtaining a sample, sized L, of the reference signal,(F=[ƒ₁, . . . , ƒ_(L)]); determining a value corresponding to a norm ofthe difference between the two samples obtained; detecting the anomalywhen said value is greater than a third threshold λ_(γ) ₁ *=λ_(γ) ₁ (τ)where the function λ_(γ) ₁ (τ) corresponds to the unique solution, in η,of the equation 1−R(τ,η)=γ₁, where the function R(τ,⋅) corresponds tothe distribution function of the square root of any unspecified randomvariable according to a non-centered . . . χ² distribution law with Ldegrees of freedom and defined by the parameter τ².
 11. The methodaccording to claim 1, wherein said observed signal corresponds to asignal belonging to the group consisting of: a signal called anelectrocardiogram signal, a signal called a electroencephalogram signal,a signal representing a progress of arterial pressure, a signalrepresenting a progress of a concentration of oxygen in the tissues, asignal representing a progress of intra-cranial pressure, a signalrepresenting the progress of a respiratory flow.
 12. The methodaccording to claim 1, wherein said physical disturbance signal X(t) isGaussian.
 13. A non-transitory storage medium comprising a computerprogram product stored thereon having program code instructions forimplementing a method for detecting presence of an anomaly Δ(t) includedin an observed physical signal Y(t) representing respiratory flow of apatient on artificial respiration and progress of a patient'sphysiological parameters, the observed signal including respirationstages of the respiratory flow including an inspiration during a firsttemporal range, which is followed by a pause during second temporalrange, which is followed by an expiration during a third temporal range,wherein when said program is executed by a computer of a detectingdevice, said observed signal comprising an addition of a physicaldisturbance signal X(t), and a reference signal ƒ(t), and said anomalybeing relative to a modification of the behavior of the reference signalƒ(t) relative to a first tolerance value (τ,τ₀), said method comprisingthe following acts performed by the detecting device: receiving theobserved physical signal by the device; and detecting, by the device,presence of the anomaly Δ(t) included in the observed physical signalY(t), wherein detecting comprises: determining a temporal set Ecomprising at least one instant of interest (t_(k); {t₁, . . . ,t_(K)}); and detecting the presence of said anomaly within said observedphysical signal in said temporal set E by carrying out a hypothesis testusing said first tolerance value (τ,τ₀), a first rate of tolerated falsealarms (γ₁), and data (p,Y) obtained from a processing of the observedsignal Y(t); wherein the temporal set E corresponds to one of the first,second or third temporal ranges.
 14. A device for detecting the presenceof an anomaly Δ(t) included in an observed physical signal Y(t)representing respiratory flow of a patient on artificial respiration,said observed signal comprising an addition of a physical disturbancesignal X(t), and a reference signal ƒ(t), and said anomaly being relatedto a modification of the reference signal ƒ(t) relative to a firstpredetermined tolerance value (τ,τ₀), said device comprising: aprocessor; and a non-transitory computer-readable medium comprisinginstructions stored thereon, which when executed by the processorconfigure the device to perform acts comprising: receiving the observedphysical signal by the device; and detecting, by the device, presence ofthe anomaly Δ(t) included in the observed physical signal Y(t), whereindetecting comprises: determining a temporal set E comprising at leastone instant of interest (t_(k); {t₁, . . . , t_(K)}); and detecting thepresence of said anomaly within said observed physical signal in saidtemporal set E by carrying out a hypothesis test using said firstpredetermined tolerance value (τ,τ₀), a first rate of tolerated falsealarms (γ₁), and data (p,Y) obtained from a processing of the observedsignal Y(t); wherein the temporal set E corresponds to one of a first,second or third temporal ranges.
 15. The device for detecting accordingto claim 14, wherein the device is further configured by theinstructions to: obtain a projected value u for said at least oneinstant of interest (t_(k)) by projecting the observed physical signalalong a vector of form p of the reference signal; and detect the anomalywhen the absolute value of said projected value u is above a thresholdλ_(γ) ₁ *=Q_(|τ+w|)(1−γ₁) where γ₁ is said rate of tolerated falsealarms, τ is said first value of tolerance, Q is a quantile function ofa random variable |τ+w| where w is a projection of said physicaldisturbance signal, along said vector of form p.